Nuprl Lemma : intuitionistic-Ramsey
∀R,T:ℕ ⟶ ℕ ⟶ ℙ. (b-almost-full(n,m.R[n;m]) ⇒ b-almost-full(n,m.T[n;m]) ⇒ b-almost-full(n,m.R[n;m] ∧ T[n;m]))
Proof
Definitions occuring in Statement :
b-almost-full: b-almost-full(n,m.R[n; m]),
nat: ℕ,
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
b-almost-full: b-almost-full(n,m.R[n; m]),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
strict-inc: StrictInc,
compose: f o g
Lemmas referenced :
strict-inc_wf,
b-almost-full_wf,
nat_wf,
b-almost-full-intersection,
compose-strict-inc
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
cut,
lemma_by_obid,
hypothesis,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
functionEquality,
cumulativity,
universeEquality,
dependent_functionElimination,
setElimination,
rename,
independent_functionElimination,
because_Cache
Latex:
\mforall{}R,T:\mBbbN{} {}\mrightarrow{} \mBbbN{} {}\mrightarrow{} \mBbbP{}.
(b-almost-full(n,m.R[n;m]) {}\mRightarrow{} b-almost-full(n,m.T[n;m]) {}\mRightarrow{} b-almost-full(n,m.R[n;m] \mwedge{} T[n;m]))
Date html generated:
2016_05_14-PM-09_53_48
Last ObjectModification:
2015_12_26-PM-09_46_56
Theory : continuity
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