Nuprl Lemma : simp_lemma1
∀[P:ℙ]. (P supposing False ⇐⇒ True)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
false: False,
true: True
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
member: t ∈ T,
prop: ℙ,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
false: False
Lemmas referenced :
isect_wf,
false_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
independent_pairFormation,
lambdaFormation,
natural_numberEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaEquality,
hypothesisEquality,
voidElimination,
rename,
universeIsType,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. (P supposing False \mLeftarrow{}{}\mRightarrow{} True)
Date html generated:
2019_10_15-AM-10_46_31
Last ObjectModification:
2018_09_27-AM-09_41_14
Theory : basic
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