Nuprl Lemma : Game-add_functionality
∀G1,H1,G2,H2:Game. (G1 ≡ G2 ⇒ H1 ≡ H2 ⇒ G1 ⊕ H1 ≡ G2 ⊕ H2)
Proof
Definitions occuring in Statement :
eq-Game: G ≡ H,
Game-add: G ⊕ H,
Game: Game,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
prop: ℙ,
implies: P ⇒ Q,
so_apply: x[s],
all: ∀x:A. B[x],
eq-Game: G ≡ H,
and: P ∧ Q,
cand: A c∧ B,
Game-add: G ⊕ H,
right-indices: right-indices(g),
left-indices: left-indices(g),
mkGame: {mkGame(f[a] with a:L | g[b] with b:R},
Wsup: Wsup(a;b),
pi1: fst(t),
pi2: snd(t),
guard: {T},
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
right-option: right-option{i:l}(g;m),
left-option: left-option{i:l}(g;m),
or: P ∨ Q
Lemmas referenced :
Game-induction,
all_wf,
Game_wf,
eq-Game_wf,
Game-add_wf,
left-indices_wf,
right-indices_wf,
or_wf,
left-option_wf,
right-option_wf,
subtype_rel_union,
left_move_add_inl_lemma,
left-move_wf,
equal_wf,
exists_wf,
right-move_wf,
left_move_add_inr_lemma,
right_move_add_inl_lemma,
right_move_add_inr_lemma,
eq-Game_inversion
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
instantiate,
hypothesis,
cumulativity,
functionEquality,
hypothesisEquality,
independent_functionElimination,
lambdaFormation,
independent_pairFormation,
unionElimination,
because_Cache,
productElimination,
dependent_functionElimination,
dependent_pairFormation,
inlEquality,
voidEquality,
applyEquality,
independent_isectElimination,
voidElimination,
isect_memberEquality,
inlFormation,
inrEquality,
inrFormation
Latex:
\mforall{}G1,H1,G2,H2:Game. (G1 \mequiv{} G2 {}\mRightarrow{} H1 \mequiv{} H2 {}\mRightarrow{} G1 \moplus{} H1 \mequiv{} G2 \moplus{} H2)
Date html generated:
2018_05_22-PM-09_53_46
Last ObjectModification:
2018_05_20-PM-10_42_11
Theory : Numbers!and!Games
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