Nuprl Lemma : qadd_functionality_wrt_qless_3
∀[a,b,c,d:ℚ]. (a + c < b + d) supposing (c < d and a < b)
Proof
Definitions occuring in Statement :
qless: r < s,
qadd: r + s,
rationals: ℚ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
qadd_functionality_wrt_qless,
qle_weakening_lt_qorder,
qless_witness,
qadd_wf,
qless_wf,
rationals_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b,c,d:\mBbbQ{}]. (a + c < b + d) supposing (c < d and a < b)
Date html generated:
2016_05_15-PM-11_00_10
Last ObjectModification:
2015_12_27-PM-07_49_12
Theory : rationals
Home
Index