Nuprl Lemma : eq-Game_weakening
∀G,H:Game. ((G = H ∈ Game) ⇒ G ≡ H)
Proof
Definitions occuring in Statement :
eq-Game: G ≡ H,
Game: Game,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
eq-Game: G ≡ H,
and: P ∧ Q,
cand: A c∧ B,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
right-option: right-option{i:l}(g;m),
left-option: left-option{i:l}(g;m),
or: P ∨ Q,
guard: {T}
Lemmas referenced :
Game-induction,
all_wf,
Game_wf,
equal_wf,
eq-Game_wf,
subtype_rel-equal,
left-indices_wf,
and_wf,
left-move_wf,
exists_wf,
right-indices_wf,
right-move_wf,
or_wf,
left-option_wf,
right-option_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
instantiate,
hypothesis,
functionEquality,
hypothesisEquality,
cumulativity,
independent_functionElimination,
lambdaFormation,
independent_pairFormation,
dependent_pairFormation,
applyEquality,
independent_isectElimination,
equalitySymmetry,
dependent_set_memberEquality,
applyLambdaEquality,
setElimination,
rename,
productElimination,
dependent_functionElimination,
inlFormation,
because_Cache,
inrFormation,
equalityTransitivity,
hyp_replacement
Latex:
\mforall{}G,H:Game. ((G = H) {}\mRightarrow{} G \mequiv{} H)
Date html generated:
2018_05_22-PM-09_53_19
Last ObjectModification:
2018_05_20-PM-10_40_20
Theory : Numbers!and!Games
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