Nuprl Lemma : not_all_sqequal
(∀[a,b:Base]. (a ~ b)) ⇒ False
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
false: False,
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
implies: P ⇒ Q,
false: False,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
base_wf,
uall_wf,
not_zero_sqequal_one
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
lemma_by_obid,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
sqequalIntensionalEquality,
hypothesisEquality
Latex:
(\mforall{}[a,b:Base]. (a \msim{} b)) {}\mRightarrow{} False
Date html generated:
2016_05_13-PM-03_19_58
Last ObjectModification:
2016_01_14-PM-04_34_46
Theory : sqequal_1
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