Nuprl Lemma : page55-again
∀U:Type. ∀P,Q:U ⟶ ℙ. ((∀x:U. ((P x) ⇒ (Q x))) ⇒ (∀x:U. (P x)) ⇒ (∀x:U. (Q x)))
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
functionEquality,
because_Cache,
cumulativity,
universeEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}U:Type. \mforall{}P,Q:U {}\mrightarrow{} \mBbbP{}. ((\mforall{}x:U. ((P x) {}\mRightarrow{} (Q x))) {}\mRightarrow{} (\mforall{}x:U. (P x)) {}\mRightarrow{} (\mforall{}x:U. (Q x)))
Date html generated:
2016_05_15-PM-07_42_18
Last ObjectModification:
2015_12_27-AM-11_13_53
Theory : general
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