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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